On conditionally defined Fibonacci and Lucas sequences and periodicity
Bull. Korean Math. Soc.
Published online February 27, 2020
Skylyn Irby and Sandra Spiroff
University of Mississippi
Abstract : We synthesize the recent work done on conditionally defined Lucas and Fibonacci numbers, tying together various definitions and results generalizing the linear recurrence relation. Allowing for any initial conditions, we determine the generating function and a Binet-like formula for the general sequence, in both the positive and negative directions, as well as relations among various sequence pairs. We also determine conditions for periodicity of these sequences and graph some recurrent figures in Python.
Keywords : generalized Fibonacci; linear recurrence, periodicity
MSC numbers : 11B-39
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